Question

The slant height of a right cone is twice the radius of the cone. The surface area of the cone is `75pi` square inches. What is the slant height and the radius of the cone?

Answer 1

`r= 5 " inches", " slant height" = 10 " inches"`

Explanation:

Given: right cone; `SA = 75 pi " inches"^2; " slant height" = l = 2r`

Surface Area of a right cone`= SA = pi r^2 + pi r l`,

where `pi r l =` lateral surface area.

`75 pi = pi r^2 + pi r l`

Factor the `pi: " " 75 pi = pi (r^2 + r l)`

Divide by `pi: " " (75 pi)/pi = ( pi (r^2 + r l))/pi`

Simplify: `" "75 = r^2 + r l`

Substitute `l = 2r: " " 75 = r^2 + r(2r)`

Simplify: `" "75 = r^2 + 2r^2`

Factor `r^2: " " 75 = r^2 (1 +2)`

Simplify: `" "75 = 3 r^2`

Divide both sides by `3: " " 25 = r^2`

Square root both sides: `" " r = 5 " inches"`

slant height `" " l = 2r = 10 " inches"`